The human eye suffers from the optical defect known as spherical aberration. Spherical aberration is the term used to describe the fact that light rays entering a refracting (focusing) surface such as the cornea are less strongly focused at the center of the refracting surface and progressively more strongly focused off center. This results in a suboptimal image. This image is not clearly focused on one focal point but instead in a series of focal points in front of the intended focal point (i.e., the retina) resulting in "blur circles."
This aberration is primarily caused by the fact that the first surface of the eye, the anterior corneal surface, is a very highly curved optical surface whose effective aperture, the pupil of the eye, typically is a sizeable fraction of the radius of curvature. Such conditions generally lead to undercorrected spherical aberration in which the outer portions of the cornea refract light more strongly than do the central portions and, hence, there is not a common focal point for the whole pupil.
Fortunately, the spherical aberration for the eye in total is less than that introduced by the cornea because the crystalline lens corrects a portion of the aberration leaving less to degrade vision by the time light reaches the retina. The crystalline lens can do this primarily because it is a gradient index. That means that the index of refraction of the crystalline lens is not constant throughout the lens but changes, increasing as light travels from the anterior surface to the center and then decreasing as light passes from the center to the posterior surface. Thus, in the crystalline lens, one may think of the rays of light as being curved inside instead of being straight as they are in common lenses. However, even though a good deal of the aberration is removed depending upon the condition of the crystalline lens, even for a good condition crystalline lens, some does remain and this could be removed by altering the anterior surface of the cornea to make it more elliptical in shape, as discussed by Campbell, C. E. in The effect of spherical aberration of contact lenses to the wearer, Am. J Optom. and Physiol. Opt., 1981, 58:212-17.
The spherical aberration induced by any convex surface is not only a function of the surface curvature but also the convergence of the light as it enters the surface. For instance, purely spherical surfaces generally introduce spherical aberration. But, if light enters a spherical surface with just the right amount of convergence, there is absolutely no spherical aberration induced. This suggests that hyperopes will, in general, exhibit less spherical aberration when corrected with spectacle lenses than will myopes because, for proper correction, light must converge as it enters the eve of a hyperope, whereas it must diverge as it enters the eye of the myope. However this is not true for the contact lens wearer, as was first pointed out by Campbell (1981), supra, and then in more detail by Atchison, J. Opt. Soc. Am., 1995, 12:2267-73.
In fact, spherical aberration is in general less for the myope than for the hyperope who is corrected with contact lenses. This is because one must think of the anterior corneal surface as being replaced by the contact lens and this alters the optical conditions from those conditions experienced when using a spectacle lens. Thus, when a myope is corrected with a contact lens, the effective anterior surface is reduced in curvature so the spherical aberration is thereby decreased. The opposite occurs for a hyperope.
Typically, the curvature of a conventional contact lens surface has been described in terms of "conic sections," which includes the sphere, parabola, ellipse, and hyperbola. All rotationally symmetric conic sections can be expressed in terms of a single equation ##EQU1## where X is the aspheric surface point at position Y, r is the central radius, and the conic constant, K, is an aspheric coefficient that relates to the shape factor, E, according to E=-K. This equation defines a curve that, when rotated about the axis Y=0, defines the surface of the conic section. Other conic constants or aspheric coefficients include the eccentricity, e, which is related to K by the equation K=-e.sup.2, and the rho factor, .rho., which is defined as 1-e.sup.2.
The value of the aspheric coefficient determines the form of the conic section. For a sphere, e=0 and K=0. An ellipse typically has an eccentricity between 0 and 1 and a K between 0 and -1. A parabola is characterized by an e=1 (i.e., K=-1). For a hyperbola, e is greater than 1 and K&lt;-1.
Conventionally, most lens surfaces are spherical or near-spherical in curvature. Theoretically, for an infinitely thin lens, a spherical curvature is ideal to sharply focus the light passing through the lens. However, the curvatures and thickness gradations of a real contact lens that provides power correction produce well-known optical aberrations, including spherical aberration, coma, distortion, and astigmatism; i.e., light from a point source passing through different areas of the lens that does not focus at a single point. This causes a certain amount of blurring. Furthermore, purely spherical lenses are not suitable for correcting astigmatic vision or for overcoming presbyopia.
Longitudinal spherical aberration of modern ophthalmic lenses was discussed by Bauer in Applied Optics, Vol. 19, No. 13 (Jul. 1, 1980). He found that longitudinal spherical aberration of those soft and hard contact lenses that have spherical surfaces is substantially larger than that of spectacle lenses. Ray tracing showed that, by applying at least one properly selected aspherical surface, the spherical aberration of contact lenses can be corrected. However, Bauer states that visual acuity is affected also by other aberrations and Bauer suggests that correction of spherical aberration does not influence visual acuity or contrast appreciably.
Nevertheless, the correction of spherical aberration has been considered to be desirable. U.S. Pat. No. 4,434,113 describes a method for spin casting lenses having a reduced spherical aberration. See, also, U.S. Pat. No. 4,564,484.
U.S. Pat. No. 4,1959,119 describes a contact lens with reduced spherical aberration for aphakic patients wherein the contact lens has a rear surface with an eccentricity of 0.5200 and a front surface having an eccentricity defined by a particular formula based on the index of refraction of the contact lens material.
U.S. Pat. No. 3,711,191 describes an ophthalmic lens having aberration correction. The ophthalmic lens has a far vision upper lens portion with a first focal power corrected for aberrations that are specific to far vision, a near vision lower lens portion with a second higher focal power corrected for aberrations that are specific to near vision, and, between those portions, an intermediate vision lens portion with a focal power that progressively varies from said first focal power to said second focal power and being corrected for aberrations specific to vision of an object point progressively drawing nearer to the lens.
U.S. Pat. No. 5,050,981 describes an aspheric lens for providing improved vision and a method for generating the lens using ray tracing techniques. The lens is characterized by a hyperbolic or parabolic surface (i.e., K less than or equal to -1) that functions to reduce spherical aberrations and minimizes the retinal image spot size. The method uses a model of the eye that can be considered as a three lens compound system containing 13 surfaces for the purpose of ray trace analysis. The lens must have one surface that is a symmetric sphere as defined by the formula above where K is less than or equal to -1. The value of the conic constant, K.kappa., is varied to obtain sharpest focus by minimizing the retinal spot size of rays traced using that particular lens/eye model system.
U.S. Pat. No. 5,191,366 describes an aspheric lens and method for producing the lens to remove spherical aberration by arbitrarily controlling the spherical aberration. Ray tracing is performed using an incident ray, a final passing point of the ray is compared with a preset desired final passing point, and a slope of a curved surface corresponding to the points of incidence of the ray is determined so that both final passing points coincide.
However, the curvature of the front surface of any soft contact lens placed on the eye will vary with its power and lens flexure. A minus lens used to correct myopia can reduce the dioptric curvature of the combined soft lens/corneal surface and as a result can reduce the spherical aberration at the eye's front surface.
It is possible for this soft lens/corneal spherical aberration to provide excessive reduction; so much so that minus lens powers cause the compensating power of the crystalline lens to be unopposed. This can result in an overall increased spherical aberration for those eyes. In the case of a plus soft contact lens, used to correct hyperopia, the increased dioptric curvature of the soft contact lens/cornea surface can also increase spherical aberration.
Thus, new and better methods for designing soft contact lenses having spherical aberration control are still being sought to provide soft contact lenses that minimize or eliminate spherical aberration.